# Topological Invariant and Quantum Spin Models from MagneticπFluxes in Correlated Topological Insulators

@article{Assaad2013TopologicalIA,
title={Topological Invariant and Quantum Spin Models from Magnetic$\pi$Fluxes in Correlated Topological Insulators},
journal={Physical Review X},
year={2013},
volume={3}
}
• Published 20 April 2012
• Physics
• Physical Review X
The adiabatic insertion of a \pi flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that \pi fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z_2 topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a \pi flux gives rise to a Kramers doublet of spinon states with a Curie law signature in the magnetic susceptibility. Electronic correlations…
9 Citations

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## References

SHOWING 1-10 OF 62 REFERENCES

### Topological insulators and Mott physics from the Hubbard interaction

• Physics
• 2010
We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions.

### Quantum spin-Hall effect and topologically invariant Chern numbers.

• Physics
Physical review letters
• 2006
It is shown that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers, and the nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM).

### Topological order and semions in a strongly correlated quantum spin Hall insulator.

• Physics
Physical review letters
• 2012
This work identifies an exotic phase for large spin-orbit coupling and intermediate Hubbard interaction that is gapped and does not break any symmetry, and argues that it has gapless edge modes protected by time-reversal symmetry but a trivial Z(2) topological invariant.

### One-dimensional topologically protected modes in topological insulators with lattice dislocations

• Physics
• 2009
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems such as the B-phase of superfluid helium He3, where vortices are

### Topological semimetal in a fermionic optical lattice

• Physics
• 2012
Experimental progress has made it possible to load fermionic atoms into higher orbital bands. Such systems provide a platform for studying quantum states of matter that have no prior analogues in

### Quantum spin liquid emerging in two-dimensional correlated Dirac fermions

• Physics
Nature
• 2010
It is shown, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermion and an antiferromagnetically ordered Mott insulator.

### Quantum spin Hall insulators with interactions and lattice anisotropy

• Physics
• 2012
We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice, combining the cellular dynamical mean-field theory and its real-space extension

### Universal probes of two-dimensional topological insulators: dislocation and π flux.

• Physics
Physical review letters
• 2012
It is conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.

### Correlation effects on a topological insulator at finite temperatures

• Physics
• 2012
We analyze the effects of the local Coulomb interaction on a topological band insulator (TBI) by applying the dynamical mean-field theory to a generalized Bernevig-Hughes-Zhang model having electron